Stepper motors are electric motors that move by increments, or steps, rather than turning smoothly as conventional electric motors. When windings of a stepper motor are energized, magnetic fields are generated and a rotor of the stepper motor turns to a certain position and stays there unless or until different windings are energized.
The stepper motor may be capable of withstanding an external torque applied to its shaft once the shaft has come to rest with current applied. This torque is typically called holding torque. The holding torque is typically at a maximum when the rotor and stator fields are orthogonal (β=90°), and in general it also varies depending on the position. This variation is caused by the detent torque, which adds and subtracts from the electrically induced torque when the shaft of the motor moves.
The difference between the produced torque and detent torque makes the motor rotate. To avoid missing a step rotation, sufficient electrical current should be forced to overcome the detent torque. Loss of the step rotation may result in a stall of the motor.
Typically, current mode driving may be implemented for driving stepper motors. Examples of monolithic circuits functioning in a current mode are the L6208 and L6228 devices available from STMicroelectronics, the A3977 available from Allegro, the TMC236 available from Trinamic, and the TB62201 available from Toshiba.
Many current mode control circuits may use a (PWM) pulse width modulation technique for regulating phase current. For this reason, hereinafter reference will be made to a PWM driving mode, though the same considerations hold similarly for an analog driving mode.
A common current mode driving technique may limit the phase current to a reference peak value using a sense comparator. This type of control is also called PWM peak current control and is illustrated in FIG. 1. Typically, this control is affected by an error due to the current ripple, the amplitude of which is hardly controllable as it may be affected by numerous factors, such as the supply voltage of the power bridge, the phase current level, the PWM switching frequency, and the electrical parameters of the motor.
In the PWM peak current control mode, the peak current value (i.e. the peak torque value) is regulated, and not its average value. Therefore, unpredictable and non-negligible error that may be introduced by the inevitable current ripple may not permit driving with a large number of micro-step divisions because the torque error may be larger than the separation between the micro-step reference values.
An alternative technique of driving brushless motors includes adjusting the drive voltage of the motor to control the average voltage applied to the phase load instead of the maximum phase current. This type of control may be implemented either by applying a continuous voltage or by PWM driving the power stage. In this case, when the motor is at rest or is moving very slowly back (electromotive force voltage is negligible), the average phase voltage is: VPHASE=VS·D where D is the duty cycle of the voltage applied to the motor phase and Vs the voltage supply of the power stage. The average phase current is:
                    I        _            PHASE        =                                        V            _                    PHASE                                      R            S                    +                      R            L                              =                                                  V              S                        ·            D                                              R              S                        +                          R              L                                      ≅                                            V              S                        ·            D                                R            L                                ,where RL is the load resistance and Rs is the resistance of a shunt resistor, if used. In this way, the average phase current may be regulated by regulating the PWM duty cycle of the power stage.
One of the main advantages of voltage mode driving is that the driving system controls the average value of the phase current and not its peak value. In FIG. 2, a basic architecture of a voltage mode driver is shown.
When the motor is running at high speed and the back-electromotive force (BEMF) is no longer negligible, the phase currents may have the same frequency and shape of the applied phase voltage and are outphased from the phase voltage by the load angle. The load angle represents the difference between stator magnetic field vector angle and rotor magnetic field vector angle and may depend on the load torque, the holding torque and the speed.
The amplitude of the BEMF may be equal to kE ·ωEL, wherein ωEL represents the electrical frequency and kE is the electric constant of the motor.
In a voltage driving mode, the amplitude of the current may not have a fixed value, but may adapt, by itself, to the load condition when the load torque varies, to reach an equilibrium state. In the voltage mode, the equation that ties the current Ieq to the load torque is:Tload(α)∝Ieq(α)·BEMF·cos(α)wherein Ieq is the resultant value of the amplitude of the two phase currents, ∝ means “proportional to”, α is equal to π/2−β and represents the angle between the BEMF voltage and the equivalent current.
In FIG. 3 a time graph of the produced mechanical power (proportional to the produced torque) is shown. Even if the phase current in voltage mode driving is not purely sinusoidal, as it may be in current mode driving, the final produced torque may not be more distorted than for a sinusoidal phase current. The reason is that, if the BEMF, as most often is the case, is not sinusoidal because of a motor geometry not being perfectly regular, then application of a purely sinusoidal phase current on the stator windings may not ensure generation of a constant torque.
In addition, the peculiarity of a voltage driving mode to produce phase currents of a constant amplitude makes the control more flexible, and the torque uniformity may be comparable to that obtained with current mode driving. Stepper driving applications may not make use of the voltage mode driving technique because of numerous significant drawbacks that may limit the effective performance of such a driving approach.
A problem with voltage mode driving may include the loss of the effective average produced torque, due the BEMF voltage when the speed of the motor increases. Such uncontrolled decreasing of average produced torque may cause loss of steps, and even the complete stall of the motor during acceleration. This issue may be very likely in stepper motors, in which the electric constant KE is relatively large in respect to other types of motors, and thus, relatively small speeds may be sufficient to generate relatively large BEMF voltages that may lead to a loss of steps.
FIG. 4 illustrates the various electrical parameters of a stepper motor driven in the voltage mode during a constant acceleration. The dashed curves are related to the other phases of the stepper motor. Following the traditional approach, where the current ratio (but also the voltage ratio) may be equal to the tangent of the motor speed, the optimal voltage waveform to be applied on the two phases may include two sinusoidal waveforms respectively outphased by 90° degrees, to produce the same torque with every rotor angle.
In terms of an equivalent electrical circuit, the BEMF voltage can be represented by a sinusoidal voltage generator in series with the phase inductance, having an amplitude proportional to the motor speed, and a frequency equal to the motor speed. The phase of the BEMF may depend on the load angle between the stator and rotor fields.
FIG. 4 shows that the increasing BEMF decreases the phase current, and that the applied torque to the rotor decreases as the speed increases. The main problem of the voltage mode approach is that the produced torque may decrease to the detent torque value, thus causing the stepper motor to lose steps, or completely stall.
In a stepper motor driven in the voltage mode, the amplitude of the phase current is typically proportional to the amplitude of the BEMF. Since the BEMF amplitude may be proportional to the rotational speed of the motor (|BEMF|=kE fEL, where fEL, is the electrical frequency of the motor in Hz), for a constant amplitude of the voltage applied to each phase winding, the amplitude of the phase current decreases when speed increases. This may cause a reduction of the produced torque, which may be insufficient to overcome the detent torque and may lead to a stall condition.
In voltage mode control systems for brushless motors (BLDC), a V/f or k·f control technique may be implemented for compensating the induced BEMF, but brushless and stepper motors are significantly different from each other. For example, BLDC motors typically have good performance while rotating. They typically operate at a relatively high speed, and the stator magnetic fluxes are typically controlled synchronously with the rotor position to adjust the load angle, thus increasing the driving efficiency and reducing the torque ripple. Stepper motors typically have good performance in assuming angular positions. They typically operate in a wide range of speeds (from fractions of step/second to thousands step/second), but their task is accurate positioning in a steady state, without missing steps. For fast positioning, they should function at a relatively high speed, and even with the problems associated with generation of a large BEMF.
These differences may make the techniques of BEMF compensation that are effectively used in driving a BLDC motor ineffective for a stepper motor. This is illustrated in FIG. 5, that illustrates a graph of the characteristics of phase current magnitude as a function of the stepping frequency Istep (motor speed).
The waveforms correspond to the resulting phase current under voltage mode driving respectively without compensation and with BLDC standard k·f compensation, where k factor is the electrical constant KE of the motor. Even using the k·f compensation, the control of the phase current may be still far from acceptable because of the large variations of the phase current at a relatively low speed, and of the significant reduction of the phase current when the speed increases.